/// <summary>
/// The y-coordinate of the intersection of the vertically projected line with the provided segment.
/// </summary>
/// <param name="xPtN">The x-coordinate of pt n, where the projection starts.</param>
/// <param name="ptI">Vertex i of the segment.</param>
/// <param name="ptJ">Vertex j of the segment.</param>
/// <returns>System.Double.</returns>
/// <exception cref="System.ArgumentException">Segment is vertical, so intersection point is either infinity or NAN.</exception>
public static double IntersectionPointY(
double xPtN,
Point ptI,
Point ptJ)
{
if (Segment.IsVertical(ptI, ptJ))
{
throw new ArgumentException("Segment is vertical, so intersection point is either infinity or NAN.");
}
return((xPtN - ptI.X) * ((ptJ.Y - ptI.Y) / (ptJ.X - ptI.X)) + ptI.Y);
}
/// <summary>
/// The numbers of shape boundary intersections a horizontal line makes when projecting to the right from the provided point.
/// If the point is on a vertex or segment, the function returns either 0 or 1.
/// </summary>
/// <param name="coordinate">The coordinate.</param>
/// <param name="shapeBoundary">The shape boundary composed of n points.</param>
/// <param name="includePointOnSegment">if set to <c>true</c> [include point on segment].</param>
/// <param name="includePointOnVertex">if set to <c>true</c> [include point on vertex].</param>
/// <param name="tolerance">The tolerance.</param>
/// <returns>System.Int32.</returns>
/// <exception cref="System.ArgumentException">Shape boundary describes a shape. Closure to the shape boundary is needed.</exception>
public static int NumberOfIntersections(
Point coordinate,
Point[] shapeBoundary,
bool includePointOnSegment = true,
bool includePointOnVertex = true,
double tolerance = GeometryLibrary.ZeroTolerance)
{
if (shapeBoundary[0] != shapeBoundary[shapeBoundary.Length - 1])
{
throw new ArgumentException("Shape boundary describes a shape. Closure to the shape boundary is needed.");
}
// 1. Check horizontal line projection from a pt. n to the right
// 2. Count # of intersections of the line with shape edges
// Note shape coordinates from XML already repeat starting node as an ending node.
// No need to handle wrap-around below.
int numberOfIntersections = 0;
for (int i = 0; i < shapeBoundary.Length - 1; i++)
{
Point vertexI = shapeBoundary[i];
if (PointIntersection.PointsOverlap(coordinate, vertexI))
{
return(includePointOnVertex ? 1 : 0);
}
Point vertexJ = shapeBoundary[i + 1];
if (!PointIsLeftOfSegmentEnd(coordinate.X, vertexI, vertexJ))
{
// Pt is to the right of the segment.
continue;
}
bool pointIsWithinSegmentHeight = PointIsWithinSegmentHeight(
coordinate.Y,
vertexI, vertexJ,
includeEnds: includePointOnSegment);
if (!pointIsWithinSegmentHeight)
{
// Point is out of vertical bounds of the segment extents.
continue;
}
bool pointIsWithinSegmentWidth = ProjectionVertical.PointIsWithinSegmentWidth(
coordinate.X,
vertexI, vertexJ,
includeEnds: includePointOnSegment);
if (Segment.IsVertical(vertexI, vertexJ))
{
if (pointIsWithinSegmentWidth)
{ // Point is on vertical segment
return(includePointOnSegment ? 1 : 0);
}
// Point hits vertical segment
numberOfIntersections++;
continue;
}
if (Segment.IsHorizontal(vertexI, vertexJ))
{ // Segment would be parallel to line projection.
// Point is collinear since it is within segment height
if (pointIsWithinSegmentWidth)
{ // Point is on horizontal segment
return(includePointOnSegment ? 1 : 0);
}
continue;
}
double xIntersection = IntersectionPointX(coordinate.Y, vertexI, vertexJ);
if (PointIsLeftOfSegmentIntersection(coordinate.X, xIntersection, vertexI, vertexJ))
{
numberOfIntersections++;
}
else if (NMath.Abs(coordinate.X - xIntersection) < tolerance)
{ // Point is on sloped segment
return(includePointOnSegment ? 1 : 0);
}
}
return(numberOfIntersections);
}